Operations Research and Financial Engineering

Operations Research and Financial Engineering at Princeton University offers a rigorous interdisciplinary graduate program designed to equip students with advanced analytical and quantitative skills necessary for solving complex problems in finance, industry, and government. This program integrates the principles of operations research—including optimization, stochastic models, and decision analysis—with cutting-edge financial engineering techniques. Students engage in a comprehensive curriculum that covers a broad range of topics such as quantitative finance, risk management, stochastic processes, mathematical modeling, and computational methods. The program emphasizes both theoretical foundations and practical application, preparing graduates for careers in financial institutions, consulting firms, government agencies, and research institutions.

The faculty comprises renowned experts in both operations research and financial engineering, fostering an environment of innovation and collaborative research. Students have access to state-of-the-art facilities and resources, including specialized research centers and industry-sponsored projects. The program also encourages interdisciplinary collaboration, allowing students to work on real-world problems using advanced mathematical and computational tools. Graduates of this program are well-equipped to analyze financial markets, develop risk assessment models, optimize investment strategies, and contribute to the development of new financial products and services.

The curriculum typically includes courses in optimization methods, financial derivatives, stochastic calculus, machine learning, and data analysis, among others. Students are also required to complete a master’s thesis or a significant research project demonstrating their proficiency in applying quantitative techniques to practical problems. The program fosters a strong foundation in quantitative reasoning, problem-solving, and analytical thinking, which are essential for leadership roles in the rapidly evolving landscape of finance and operations management. Graduates from Princeton’s Operations Research and Financial Engineering program are highly sought after across the financial industry, consulting, and academia, making it a premier choice for aspiring quantitative professionals.

Courses:

The course requirements are fulfilled by successfully completing ten one-semester courses, two of which are required research courses (ORF 509 and 510).

Thesis:

The M.S.E. program has a strong research focus reflected in the requirement of a thesis. Upon completion and acceptance of the thesis by the department

• FIN 501 Asset Pricing I: Pricing Models and Derivatives 
• ORF 504 Financial Econometrics 
• ORF 505 Statistical Analysis of Financial Data 
• ORF 509 Directed Research IUnder the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 one semester prior to taking the general examination.
• ORF 510 Directed Research IIUnder the direction of a faculty member, Ph.D. and M.S.E. students carry out research, write a report each, and present the results. Of these, 509 is normally taken during the first year of study. Doctoral students should complete 510 one semester prior to taking the general examination.
• ORF 511 Extramural Summer ProjectSummer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor, that will provide practical experience relevant to the student's course of study. Start date no earlier than June 1. A research report and sponsor's evaluation are required.
• ORF 515 Asset Pricing II: Stochastic Calculus and Advanced Derivatives (also 
• ORF 522 Linear and Nonlinear OptimizationTheoretical concepts underlying linear programming, with computer implementations of some of the different methods. The topics covered include duality theory, the simplex method, interior point methods, related numerical issues, and modeling paradigms.
• ORF 523 Convex and Conic OptimizationAn introduction to the central concepts needed for studying the theory, algorithms, and applications of nonlinear optimization problems. Topics covered include first- and second-order optimality conditions; unconstrained methods, including steepest descent, conjugate gradient, and quasi-Newtonian methods; constrained active-set methods; and duality theory and Lagrangian methods. Prerequisite: linear optimization.
• ORF 524 Statistical Theory and MethodsA graduate level introduction to statistical theory and methods. It introduces some of the most important and commonly-used principles of statistical inference and covers the statistical theory and methods for point estimation, confidence intervals, and hypothesis testing, and the applications of the fundamental theory to linear models and categorical data.
• ORF 525 Statistical Learning and Nonparametric EstimationAn introduction to the most important and broadly utilized statistical methods used in many scienti¿c data analysis, including general linear, mixed-e¿ects, generalized linear models, regression and ANOVA models. The methodological power of statistics will be emphasized. Objectives of this course are to give students a solid understanding of these methods, and o¿er them experience in applying these methods to real data using statistical computing packages and interpreting results. For master's/Ph.D. students and advanced undergraduates.
• ORF 526 Probability TheoryGraduate introduction to probability theory beginning with a review of measure and integration. Topics include random variables, expectation, characteristic functions, law of large numbers, central limit theorem, conditioning, martin- gales, Markov chains, and Poisson processes.
• ORF 527 Stochastic CalculusAn introduction to stochastic analysis based on Brownian motion. Topics include local martingales, the Ito integral and calculus, stochastic differential equations, the Feynman-Kac formula, representation theorems, Girsanov theory, and applications in finance.
• ORF 531 Computational Finance in C++ 
• ORF 534 Quantitative Investment Management 
• ORF 535 Financial Risk Management
• ORF 538 PDE Methods for Financial MathematicsAn introduction to analytical and computational methods common to financial engineering problems. Aimed at PhD students and advanced masters students who have studied stochastic calculus, the course focuses on uses of partial differential equations: their appearance in pricing financial derivatives, their connection with Markov processes, their occurrence as Hamilton-Jacobi-Bellman equations in stochastic control problems, and analytical, asymptotic, and numerical techniques for their solution.
• ORF 542 Stochastic Control and Stochastic Differential GamesDeterministic optimal control, dynamic programming, and Pontryagin maximum principle. Controlled diffusion processes and stochastic dynamic programming. Hamilton-Jacobi-Bellman equation, viscosity solutions. Merton problem, singular optimal control, option pricing via utility maximization.
• ORF 544 Stochastic OptimizationThis course provides a unified presentation of stochastic optimization, cutting across classical fields including dynamic programming (including Markov decision processes), stochastic programming, (discrete time) stochastic control, model predictive control, stochastic search, and robust/risk averse optimization, as well as related fields such as reinforcement learning and approximate dynamic programming. Also covered are both offline and online learning problems. Considerable emphasis is placed on modeling and computation.
• ORF 548 Large-scale OptimizationSurvey of methods for solving large-scale optimization problems, with an emphasis on implementation issues. Topics are chosen from the following: linear programming-basis partitioning methods, Dantzig-Wolfe decomposition, Benders' decomposition, and interior point methods; nonlinear programming-conjugate gradient algorithms, quasi-Newton methods, sparse Newton methods, reduced gradient techniques, and trust-region strategies; and parallel optimization-distributed algorithms and single-machine algorithms.
• ORF 550 Topics in Probability
• ORF 551 Random Measures and Levy Processes 
• ORF 553 Stochastic Differential EquationsThe general theory of martingales and semimartingales; stochastic integrals and stochastic differential equations; diffusion processes; Brownian flows, mass transport by flows.
• ORF 554 Markov ProcessesMarkov processes with general state spaces; transition semigroups, generators, resolvants; hitting times, jumps, and Levy systems; additive functionals and random time changes; killing and creation of Markovian motions.
• ORF 557 Stochastic Analysis SeminarRecent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging.
• ORF 558 Stochastic Analysis SeminarRecent developments in the theory and applications of the analysis of random processes and random fields. Applications include financial engineering, transport by stochastic flows, and statistical imaging.
• ORF 562 Transportation and Logistics PlanningOperations research in transportation, logistics, and operations planning; static, dynamic, and stochastic inventory models; multilocational inventory methods and their extention to dynamic fleet management; dynamic routing over transportation networks; equilibrium models for traffic assignment; and the vehicle routing problem. The focus of the course is the modeling process, and the formulation and solution of mathematical problems that arise in an operational context. Additional techniques are introduced as needed. The course is open to advanced undergraduates. Prerequisites: optimization and stochastic models.
• ORF 566 High Dimensional StatisticsCourse is on statistical theory and methods for high-dimensional statistical learning and inferences arising from processing massive data from various scientific disciplines. Emphasis is given to penalized likelihood methods, independence screening, large covariance modeling, and large-scale hypothesis testing. The important theoretical results are proved.
• ORF 569 Special Topics in Statistics and Operations ResearchAdvanced topics in statistics and operations research or the investigation of problems of current interest.
• ORF 570 Special Topics in Statistics and Operations ResearchAdvanced topics in statistics and operations research or the investigation of problems of current interest.
• ORF 574 Special Topics in Investment Science
• ORF 575 Financial Engineering Seminar

• Statement of Academic Purpose
• Application Fee: $90
• Resume/Curriculum Vitae
• Recommendation Letters
• Transcripts
• Fall Semester Grades
• All applicants are required to select a subplan when applying.
• All applicants are required to submit a GRE general test. A mathematics subject test is strongly recommended.
• M.S.E. applicants are required to have the endorsement of a faculty member who is willing to supervise them prior to submitting an application.
• M.S.E. applicants are required to submit a Statement of Financial Resources.

Financing for the Operations Research and Financial Engineering (ORFE) program at Princeton University is primarily provided through a combination of merit-based fellowships, research assistantships, teaching assistantships, and external funding sources. Graduate students admitted to the program are highly competitive and often receive financial support that covers tuition and provides a stipend to support living expenses. The university offers a limited number of fellowships that are awarded based on academic excellence, research potential, and contributions to the university community. These fellowships do not require a separate application and are renewable annually, contingent upon satisfactory academic progress.

Research assistantships are another key source of funding, allowing students to work directly with faculty members on funded research projects in areas such as optimization, statistical modeling, financial engineering, and operations analysis. These positions provide a stipend aligned with the university’s graduate student pay scales and often include tuition remission. Teaching assistantships are also available, wherein students assist in undergraduate or graduate courses, gaining teaching experience while receiving financial support.

In addition to university-based funding, students may seek external grants, scholarships, and fellowships from government agencies, industry, and private foundations. The school actively supports students in applying for such opportunities, which can supplement existing financial aid packages.

Financial aid for graduate students in ORFE is competitive, and prospective applicants are encouraged to demonstrate strong academic records, research interests aligned with faculty expertise, and clear professional goals. International students are fully eligible for the same funding opportunities as domestic students, provided they meet the application requirements.

Princeton University is committed to ensuring that financial constraints do not hinder talented individuals from pursuing advanced studies in Operations Research and Financial Engineering. The university’s comprehensive funding packages aim to make graduate education accessible and sustainable. Prospective and current students are advised to consult the official Princeton University Graduate School website and the ORFE department pages for detailed, updated information on funding opportunities, application procedures, and deadlines.

The Operations Research and Financial Engineering (ORFE) program at Princeton University is a highly interdisciplinary and rigorous academic offering designed to prepare students for careers in finance, consulting, academia, and government. The program combines principles from applied mathematics, economics, statistics, and computer science to analyze complex systems and make optimal decisions in uncertain environments. Students engaging in ORFE develop a deep understanding of stochastic processes, optimization techniques, and financial modeling, equipping them with skills to address real-world problems involving large datasets and intricate models. The curriculum emphasizes both theoretical foundations and practical applications, ensuring graduates are well-versed in quantitative analysis, risk management, and financial engineering. Faculty involved in ORFE are leaders in their fields, often contributing to groundbreaking research that advances financial theory and operational efficiencies. The program encourages collaborative projects, internships, and research initiatives to enhance experiential learning. Students have access to state-of-the-art resources, including specialized laboratories and computational facilities, enabling them to apply their knowledge to current challenges in finance and operations. The degree prepares alumni for diverse roles in hedge funds, investment banks, consultancy firms, and research institutions, reflecting its versatile and comprehensive training approach. Admission is competitive, emphasizing applicants with strong quantitative skills and academic excellence. The program generally culminates in a Master’s degree, but opportunities for further academic pursuit, including PhD studies, are available for exceptional candidates. Overall, Princeton’s ORFE program stands out for its combination of rigorous academics, innovative research, and extensive industry connections, making it one of the premier programs globally for those interested in operational research and financial engineering.